Tiger Tiger Regression
Marketing Analytics
11488, LSE
11488, LSE
Loading packages we’ll need
#Installs required package for reading a csv data file
if(!require(readr)) install.packages("readr",repos = "http://cran.us.r-project.org")
library(readr)
#Installs required packages for plotting
if(!require(ggplot2)) install.packages("ggplot2",repos = "http://cran.us.r-project.org")
if(!require(gpairs)) install.packages("gpairs",repos = "http://cran.us.r-project.org")
if(!require(corrplot)) install.packages("corrplot",repos = "http://cran.us.r-project.org")
if(!require(coefplot)) install.packages("coefplot",repos = "http://cran.us.r-project.org")
if(!require(effects)) install.packages("effects",repos = "http://cran.us.r-project.org")Loading and reading data
Tiger <- read_csv("/Users/ayandacollins/Desktop/MISDI/Marketing Analytics/11488_Marketing Analytics Final Exam/Tiger Tiger Regression data.csv")
#View(Tiger)Now we will turn to examining the data. Start off by writing:
summary(Tiger)## Oveerall.Satisfaction Price Music.DJ Atmosphere
## Min. :1.000 Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000
## Median :3.000 Median :3.000 Median :3.000 Median :3.000
## Mean :2.931 Mean :3.011 Mean :2.966 Mean :3.058
## 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000 Max. :5.000
## Location Crowd.levels Special.promotions Events
## Min. :1.000 Min. :1 Min. :1.000 Min. :1.000
## 1st Qu.:3.000 1st Qu.:2 1st Qu.:2.000 1st Qu.:2.000
## Median :4.000 Median :3 Median :3.000 Median :3.000
## Mean :3.885 Mean :3 Mean :2.816 Mean :2.908
## 3rd Qu.:5.000 3rd Qu.:4 3rd Qu.:3.250 3rd Qu.:4.000
## Max. :5.000 Max. :5 Max. :5.000 Max. :5.000
## Clientele.types Venue.staff Service.facilities
## Min. :1.000 Min. :1.000 Min. :1.000
## 1st Qu.:2.000 1st Qu.:2.000 1st Qu.:2.000
## Median :2.000 Median :3.000 Median :3.000
## Mean :2.471 Mean :2.632 Mean :2.954
## 3rd Qu.:3.250 3rd Qu.:3.250 3rd Qu.:4.000
## Max. :5.000 Max. :5.000 Max. :5.000Another useful command to examine the structure of the data, i.e., the types of the variables, is str:
str(Tiger)## spec_tbl_df[,11] [88 × 11] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ Oveerall.Satisfaction: num [1:88] 4 4 1 4 4 4 4 4 2 5 ...
## $ Price : num [1:88] 3 3 4 4 3 4 4 4 2 2 ...
## $ Music.DJ : num [1:88] 3 4 3 4 3 4 5 3 3 3 ...
## $ Atmosphere : num [1:88] 3 5 3 3 3 5 5 3 1 5 ...
## $ Location : num [1:88] 4 4 4 2 4 4 5 4 1 5 ...
## $ Crowd.levels : num [1:88] 2 4 2 4 4 4 2 4 3 5 ...
## $ Special.promotions : num [1:88] 2 3 5 3 4 3 2 2 2 2 ...
## $ Events : num [1:88] 3 3 3 4 3 4 2 2 2 2 ...
## $ Clientele.types : num [1:88] 3 3 3 3 4 3 4 2 1 3 ...
## $ Venue.staff : num [1:88] 3 4 1 4 4 4 5 2 3 5 ...
## $ Service.facilities : num [1:88] 4 3 3 3 3 5 5 3 1 4 ...
## - attr(*, "spec")=
## .. cols(
## .. Oveerall.Satisfaction = col_double(),
## .. Price = col_double(),
## .. Music.DJ = col_double(),
## .. Atmosphere = col_double(),
## .. Location = col_double(),
## .. Crowd.levels = col_double(),
## .. Special.promotions = col_double(),
## .. Events = col_double(),
## .. Clientele.types = col_double(),
## .. Venue.staff = col_double(),
## .. Service.facilities = col_double()
## .. )library(lattice)
histogram(~Oveerall.Satisfaction, Tiger)
Running regressions
Pr(>|t|) gives you the p-value for that t-test
the p-value is the chance that the result you’re seeing happened due to random variation. Commonly a p-value of .05 or less (interpreted roughly as “there’s a 5% chance or less of this happening just due to random variation”) is taken to mean that the result is significant.
- the p-value is a probability conditional on assuming the null hypothesis (it’s not some unconditional “chance” (2) rather it’s the chance–under the null hypothesis–that your result would fall within a “critical region” for the hypothesis test.
2e-16 is scientific notation. e stands for exponent of 10, and it’s always followed by another number, which is the value of the exponent.2.2e-16 is the scientific notation of 0.00000000000000022, meaning it is very close to zero For example, a calculator would show the number 25 trillion as either 2.5E13 or 2.5e13.
The asterisks following the Pr(>|t|) provide a visually accessible way of assessing whether the statistic met various 𝛼 criterions.
A t-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups, which may be related in certain features. It is mostly used when the data sets, like the data set recorded as the outcome from flipping a coin 100 times, would follow a normal distribution and may have unknown variances. A t-test is used as a hypothesis testing tool, which allows testing of an assumption applicable to a population.
Mathematically, the t-test takes a sample from each of the two sets and establishes the problem statement by assuming a null hypothesis that the two means are equal. Based on the applicable formulas, certain values are calculated and compared against the standard values, and the assumed null hypothesis is accepted or rejected accordingly.
If the null hypothesis qualifies to be rejected, it indicates that data readings are strong and are probably not due to chance.
Coefficient: A number used to multiply a variable
regr1 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities, data=Tiger)
summary(regr1) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities, data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.53546 -0.24757 0.00299 0.25359 1.54773
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.008871 0.316921 -0.028 0.97774
## Price 0.062430 0.072404 0.862 0.39123
## Music.DJ 0.195764 0.067766 2.889 0.00502 **
## Atmosphere 0.201801 0.079367 2.543 0.01301 *
## Location -0.026819 0.064163 -0.418 0.67713
## Crowd.levels 0.190883 0.072348 2.638 0.01008 *
## Special.promotions -0.047656 0.075446 -0.632 0.52948
## Events 0.046119 0.083202 0.554 0.58098
## Clientele.types 0.190951 0.076420 2.499 0.01460 *
## Venue.staff 0.160862 0.063649 2.527 0.01354 *
## Service.facilities 0.064545 0.069540 0.928 0.35622
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5113 on 77 degrees of freedom
## Multiple R-squared: 0.7648, Adjusted R-squared: 0.7342
## F-statistic: 25.04 on 10 and 77 DF, p-value: < 2.2e-16regr2 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Music.DJ*Atmosphere, data=Tiger)
summary(regr2) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Music.DJ * Atmosphere,
## data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.5695 -0.2322 0.0063 0.2445 1.5736
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.22282 0.46973 -0.474 0.6366
## Price 0.06179 0.07270 0.850 0.3980
## Music.DJ 0.28161 0.15444 1.823 0.0722 .
## Atmosphere 0.27608 0.14402 1.917 0.0590 .
## Location -0.01899 0.06565 -0.289 0.7732
## Crowd.levels 0.17980 0.07481 2.403 0.0187 *
## Special.promotions -0.05224 0.07611 -0.686 0.4945
## Events 0.04491 0.08356 0.537 0.5925
## Clientele.types 0.19298 0.07680 2.513 0.0141 *
## Venue.staff 0.15840 0.06403 2.474 0.0156 *
## Service.facilities 0.07696 0.07264 1.059 0.2927
## Music.DJ:Atmosphere -0.02814 0.04545 -0.619 0.5376
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5134 on 76 degrees of freedom
## Multiple R-squared: 0.766, Adjusted R-squared: 0.7321
## F-statistic: 22.61 on 11 and 76 DF, p-value: < 2.2e-16regr3 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Clientele.types*Atmosphere, data=Tiger)
summary(regr3) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Clientele.types * Atmosphere,
## data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.58716 -0.20612 0.00239 0.22814 1.64503
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.31479 0.42162 -0.747 0.45760
## Price 0.06508 0.07235 0.900 0.37118
## Music.DJ 0.19042 0.06785 2.806 0.00636 **
## Atmosphere 0.31119 0.12729 2.445 0.01681 *
## Location -0.03068 0.06417 -0.478 0.63399
## Crowd.levels 0.19198 0.07226 2.657 0.00961 **
## Special.promotions -0.04886 0.07535 -0.648 0.51864
## Events 0.04182 0.08318 0.503 0.61661
## Clientele.types 0.34610 0.16057 2.155 0.03429 *
## Venue.staff 0.15894 0.06359 2.499 0.01459 *
## Service.facilities 0.07428 0.07001 1.061 0.29205
## Atmosphere:Clientele.types -0.04729 0.04306 -1.098 0.27558
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5106 on 76 degrees of freedom
## Multiple R-squared: 0.7685, Adjusted R-squared: 0.735
## F-statistic: 22.93 on 11 and 76 DF, p-value: < 2.2e-16regr4 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Clientele.types*Music.DJ, data=Tiger)
summary(regr4) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Clientele.types * Music.DJ,
## data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.57343 -0.24301 0.00638 0.24277 1.57624
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.20705 0.47970 -0.432 0.6672
## Price 0.06662 0.07313 0.911 0.3652
## Music.DJ 0.26145 0.13704 1.908 0.0602 .
## Atmosphere 0.19834 0.07997 2.480 0.0153 *
## Location -0.02860 0.06454 -0.443 0.6589
## Crowd.levels 0.19186 0.07270 2.639 0.0101 *
## Special.promotions -0.04208 0.07646 -0.550 0.5837
## Events 0.03728 0.08510 0.438 0.6626
## Clientele.types 0.27534 0.17099 1.610 0.1115
## Venue.staff 0.15724 0.06427 2.446 0.0167 *
## Service.facilities 0.07901 0.07461 1.059 0.2929
## Music.DJ:Clientele.types -0.02849 0.05159 -0.552 0.5824
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5136 on 76 degrees of freedom
## Multiple R-squared: 0.7657, Adjusted R-squared: 0.7318
## F-statistic: 22.58 on 11 and 76 DF, p-value: < 2.2e-16regr5 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Clientele.types*Venue.staff, data=Tiger)
summary(regr5) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Clientele.types * Venue.staff,
## data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.52675 -0.24683 0.00585 0.25559 1.53866
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.019466 0.419751 0.046 0.96313
## Price 0.062613 0.072895 0.859 0.39307
## Music.DJ 0.195686 0.068209 2.869 0.00533 **
## Atmosphere 0.202068 0.079923 2.528 0.01354 *
## Location -0.026543 0.064634 -0.411 0.68247
## Crowd.levels 0.191162 0.072866 2.623 0.01051 *
## Special.promotions -0.047758 0.075942 -0.629 0.53131
## Events 0.046761 0.083969 0.557 0.57924
## Clientele.types 0.177580 0.149968 1.184 0.24006
## Venue.staff 0.149484 0.126908 1.178 0.24251
## Service.facilities 0.063003 0.071548 0.881 0.38133
## Clientele.types:Venue.staff 0.004897 0.047153 0.104 0.91756
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5146 on 76 degrees of freedom
## Multiple R-squared: 0.7648, Adjusted R-squared: 0.7308
## F-statistic: 22.47 on 11 and 76 DF, p-value: < 2.2e-16regr6 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Crowd.levels*Atmosphere, data=Tiger)
summary(regr6) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Crowd.levels * Atmosphere,
## data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.51574 -0.25258 -0.00397 0.26176 1.49163
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.30212 0.54433 0.555 0.5805
## Price 0.06072 0.07268 0.835 0.4061
## Music.DJ 0.21223 0.07190 2.952 0.0042 **
## Atmosphere 0.08908 0.17884 0.498 0.6199
## Location -0.02791 0.06439 -0.433 0.6659
## Crowd.levels 0.06979 0.18672 0.374 0.7096
## Special.promotions -0.05099 0.07584 -0.672 0.5034
## Events 0.06131 0.08622 0.711 0.4792
## Clientele.types 0.18640 0.07694 2.423 0.0178 *
## Venue.staff 0.16086 0.06386 2.519 0.0139 *
## Service.facilities 0.05540 0.07097 0.781 0.4375
## Atmosphere:Crowd.levels 0.03728 0.05296 0.704 0.4836
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.513 on 76 degrees of freedom
## Multiple R-squared: 0.7663, Adjusted R-squared: 0.7325
## F-statistic: 22.66 on 11 and 76 DF, p-value: < 2.2e-16regr7 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Crowd.levels*Location, data=Tiger)
summary(regr7) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Crowd.levels * Location,
## data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.4892 -0.2391 -0.0531 0.2875 1.3848
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.37711 0.74580 1.847 0.06871 .
## Price 0.07961 0.07145 1.114 0.26868
## Music.DJ 0.20691 0.06663 3.105 0.00267 **
## Atmosphere 0.17384 0.07897 2.201 0.03075 *
## Location -0.40502 0.19542 -2.073 0.04160 *
## Crowd.levels -0.34396 0.27109 -1.269 0.20839
## Special.promotions -0.05428 0.07401 -0.733 0.46552
## Events 0.10119 0.08587 1.178 0.24231
## Clientele.types 0.19021 0.07489 2.540 0.01313 *
## Venue.staff 0.17620 0.06282 2.805 0.00639 **
## Service.facilities 0.02870 0.07037 0.408 0.68450
## Location:Crowd.levels 0.13678 0.06691 2.044 0.04441 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5011 on 76 degrees of freedom
## Multiple R-squared: 0.777, Adjusted R-squared: 0.7448
## F-statistic: 24.08 on 11 and 76 DF, p-value: < 2.2e-16if(!require(jtools)) install.packages("jtools",repos = "http://cran.us.r-project.org")
library(jtools)
library(interactions)
interact_plot(regr7, pred = Crowd.levels, modx = Location)
regr8 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Crowd.levels*Music.DJ, data=Tiger)
summary(regr8) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Crowd.levels * Music.DJ,
## data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.57806 -0.22686 0.00483 0.23744 1.54460
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.29133 0.54548 -0.534 0.5948
## Price 0.06834 0.07327 0.933 0.3539
## Music.DJ 0.29670 0.17233 1.722 0.0892 .
## Atmosphere 0.19022 0.08172 2.328 0.0226 *
## Location -0.02801 0.06444 -0.435 0.6651
## Crowd.levels 0.30478 0.19286 1.580 0.1182
## Special.promotions -0.04012 0.07665 -0.523 0.6022
## Events 0.03141 0.08665 0.362 0.7180
## Clientele.types 0.19769 0.07744 2.553 0.0127 *
## Venue.staff 0.15639 0.06428 2.433 0.0173 *
## Service.facilities 0.06893 0.07015 0.983 0.3289
## Music.DJ:Crowd.levels -0.03536 0.05546 -0.637 0.5257
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5133 on 76 degrees of freedom
## Multiple R-squared: 0.766, Adjusted R-squared: 0.7322
## F-statistic: 22.62 on 11 and 76 DF, p-value: < 2.2e-16regr9 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Crowd.levels*Price, data=Tiger)
summary(regr9) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Crowd.levels * Price,
## data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.4691 -0.2681 -0.0111 0.2781 1.4969
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.48856 0.60666 0.805 0.42314
## Price -0.10291 0.18655 -0.552 0.58281
## Music.DJ 0.19154 0.06794 2.819 0.00614 **
## Atmosphere 0.19551 0.07967 2.454 0.01642 *
## Location -0.01885 0.06473 -0.291 0.77169
## Crowd.levels 0.01355 0.19808 0.068 0.94566
## Special.promotions -0.05734 0.07615 -0.753 0.45378
## Events 0.04630 0.08324 0.556 0.57970
## Clientele.types 0.19964 0.07699 2.593 0.01140 *
## Venue.staff 0.16238 0.06370 2.549 0.01281 *
## Service.facilities 0.06317 0.06959 0.908 0.36690
## Price:Crowd.levels 0.05954 0.06191 0.962 0.33921
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5116 on 76 degrees of freedom
## Multiple R-squared: 0.7676, Adjusted R-squared: 0.734
## F-statistic: 22.82 on 11 and 76 DF, p-value: < 2.2e-16regr10 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Crowd.levels*Special.promotions, data=Tiger)
summary(regr10) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Crowd.levels * Special.promotions,
## data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.33868 -0.26688 -0.01333 0.28043 1.44412
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.57791 0.57449 1.006 0.31763
## Price 0.05909 0.07222 0.818 0.41582
## Music.DJ 0.19391 0.06757 2.870 0.00531 **
## Atmosphere 0.21632 0.08000 2.704 0.00845 **
## Location -0.01308 0.06494 -0.201 0.84085
## Crowd.levels -0.01952 0.18656 -0.105 0.91693
## Special.promotions -0.27658 0.20174 -1.371 0.17442
## Events 0.05866 0.08357 0.702 0.48488
## Clientele.types 0.18081 0.07663 2.360 0.02086 *
## Venue.staff 0.15990 0.06345 2.520 0.01383 *
## Service.facilities 0.05034 0.07028 0.716 0.47604
## Crowd.levels:Special.promotions 0.07387 0.06041 1.223 0.22515
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5097 on 76 degrees of freedom
## Multiple R-squared: 0.7693, Adjusted R-squared: 0.7359
## F-statistic: 23.04 on 11 and 76 DF, p-value: < 2.2e-16regr11 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Crowd.levels*Events, data=Tiger)
summary(regr11) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Crowd.levels * Events,
## data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.56672 -0.23811 -0.00309 0.23576 1.56990
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.18076 0.52474 -0.344 0.73145
## Price 0.06368 0.07286 0.874 0.38486
## Music.DJ 0.19376 0.06831 2.837 0.00584 **
## Atmosphere 0.19960 0.07998 2.496 0.01473 *
## Location -0.03415 0.06692 -0.510 0.61133
## Crowd.levels 0.26092 0.18480 1.412 0.16205
## Special.promotions -0.04424 0.07631 -0.580 0.56381
## Events 0.11133 0.17893 0.622 0.53568
## Clientele.types 0.19330 0.07705 2.509 0.01424 *
## Venue.staff 0.15630 0.06495 2.407 0.01853 *
## Service.facilities 0.07516 0.07451 1.009 0.31629
## Crowd.levels:Events -0.02451 0.05946 -0.412 0.68130
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5141 on 76 degrees of freedom
## Multiple R-squared: 0.7653, Adjusted R-squared: 0.7313
## F-statistic: 22.53 on 11 and 76 DF, p-value: < 2.2e-16regr12 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Crowd.levels*Service.facilities, data=Tiger)
summary(regr12) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Crowd.levels * Service.facilities,
## data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.5049 -0.2693 -0.0063 0.2797 1.3707
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.70333 0.60745 1.158 0.25056
## Price 0.07358 0.07245 1.016 0.31305
## Music.DJ 0.21501 0.06883 3.124 0.00253 **
## Atmosphere 0.19128 0.07929 2.412 0.01826 *
## Location -0.03103 0.06387 -0.486 0.62856
## Crowd.levels -0.04770 0.18826 -0.253 0.80066
## Special.promotions -0.05722 0.07534 -0.759 0.44993
## Events 0.03918 0.08288 0.473 0.63777
## Clientele.types 0.18899 0.07600 2.487 0.01509 *
## Venue.staff 0.16135 0.06329 2.549 0.01281 *
## Service.facilities -0.17577 0.18838 -0.933 0.35375
## Crowd.levels:Service.facilities 0.07923 0.05777 1.371 0.17428
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5084 on 76 degrees of freedom
## Multiple R-squared: 0.7705, Adjusted R-squared: 0.7372
## F-statistic: 23.19 on 11 and 76 DF, p-value: < 2.2e-16regr13 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Price*Location, data=Tiger)
summary(regr13) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Price * Location, data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.54184 -0.25268 0.00515 0.22770 1.57762
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.25700 0.76932 -0.334 0.73926
## Price 0.15374 0.26776 0.574 0.56755
## Music.DJ 0.19420 0.06830 2.843 0.00573 **
## Atmosphere 0.20254 0.07985 2.537 0.01325 *
## Location 0.04121 0.20253 0.203 0.83930
## Crowd.levels 0.18915 0.07293 2.594 0.01138 *
## Special.promotions -0.04609 0.07601 -0.606 0.54608
## Events 0.04147 0.08470 0.490 0.62585
## Clientele.types 0.19382 0.07728 2.508 0.01428 *
## Venue.staff 0.16112 0.06402 2.517 0.01395 *
## Service.facilities 0.06567 0.07001 0.938 0.35122
## Price:Location -0.02394 0.06755 -0.354 0.72404
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5142 on 76 degrees of freedom
## Multiple R-squared: 0.7652, Adjusted R-squared: 0.7312
## F-statistic: 22.51 on 11 and 76 DF, p-value: < 2.2e-16regr14 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Price*Special.promotions, data=Tiger)
summary(regr14) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Price * Special.promotions,
## data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.47309 -0.25970 -0.00744 0.26399 1.59358
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.27941 0.53972 -0.518 0.60618
## Price 0.15706 0.16893 0.930 0.35546
## Music.DJ 0.19105 0.06846 2.791 0.00665 **
## Atmosphere 0.19756 0.07998 2.470 0.01575 *
## Location -0.02747 0.06443 -0.426 0.67111
## Crowd.levels 0.19538 0.07300 2.677 0.00911 **
## Special.promotions 0.06213 0.19244 0.323 0.74771
## Events 0.04203 0.08380 0.502 0.61739
## Clientele.types 0.19884 0.07777 2.557 0.01256 *
## Venue.staff 0.16102 0.06391 2.520 0.01384 *
## Service.facilities 0.06266 0.06989 0.897 0.37277
## Price:Special.promotions -0.03524 0.05678 -0.621 0.53674
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5134 on 76 degrees of freedom
## Multiple R-squared: 0.766, Adjusted R-squared: 0.7321
## F-statistic: 22.61 on 11 and 76 DF, p-value: < 2.2e-16regr15 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Price*Events, data=Tiger)
summary(regr15) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Price * Events, data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.54087 -0.26234 0.00003 0.25901 1.51650
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.152136 0.595715 0.255 0.79912
## Price 0.005682 0.191742 0.030 0.97644
## Music.DJ 0.195198 0.068187 2.863 0.00543 **
## Atmosphere 0.200389 0.079955 2.506 0.01434 *
## Location -0.023160 0.065546 -0.353 0.72481
## Crowd.levels 0.190260 0.072799 2.613 0.01080 *
## Special.promotions -0.048692 0.075958 -0.641 0.52343
## Events -0.010538 0.195866 -0.054 0.95724
## Clientele.types 0.192096 0.076953 2.496 0.01472 *
## Venue.staff 0.157344 0.064961 2.422 0.01781 *
## Service.facilities 0.065343 0.069993 0.934 0.35348
## Price:Events 0.019731 0.061672 0.320 0.74989
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5143 on 76 degrees of freedom
## Multiple R-squared: 0.7651, Adjusted R-squared: 0.7311
## F-statistic: 22.5 on 11 and 76 DF, p-value: < 2.2e-16regr16 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Price*Clientele.types, data=Tiger)
summary(regr16) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Price * Clientele.types,
## data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.53559 -0.23367 0.00791 0.23225 1.61445
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.43135 0.46577 -0.926 0.35732
## Price 0.20800 0.13827 1.504 0.13665
## Music.DJ 0.20847 0.06832 3.051 0.00314 **
## Atmosphere 0.20443 0.07913 2.584 0.01170 *
## Location -0.02760 0.06395 -0.432 0.66721
## Crowd.levels 0.17889 0.07276 2.459 0.01622 *
## Special.promotions -0.03875 0.07554 -0.513 0.60941
## Events 0.04420 0.08294 0.533 0.59567
## Clientele.types 0.37670 0.16868 2.233 0.02847 *
## Venue.staff 0.16190 0.06344 2.552 0.01272 *
## Service.facilities 0.05984 0.06941 0.862 0.39134
## Price:Clientele.types -0.06345 0.05141 -1.234 0.22094
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5096 on 76 degrees of freedom
## Multiple R-squared: 0.7694, Adjusted R-squared: 0.736
## F-statistic: 23.05 on 11 and 76 DF, p-value: < 2.2e-16regr17 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Price*Service.facilities, data=Tiger)
summary(regr17) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Price * Service.facilities,
## data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.55327 -0.22748 -0.00276 0.24997 1.61701
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.45698 0.57519 -0.794 0.42939
## Price 0.22212 0.18571 1.196 0.23541
## Music.DJ 0.21345 0.07042 3.031 0.00333 **
## Atmosphere 0.20386 0.07946 2.565 0.01227 *
## Location -0.02490 0.06425 -0.387 0.69949
## Crowd.levels 0.18107 0.07317 2.475 0.01556 *
## Special.promotions -0.05020 0.07556 -0.664 0.50843
## Events 0.04829 0.08330 0.580 0.56387
## Clientele.types 0.19198 0.07649 2.510 0.01421 *
## Venue.staff 0.15595 0.06392 2.440 0.01702 *
## Service.facilities 0.21938 0.17981 1.220 0.22622
## Price:Service.facilities -0.05638 0.06037 -0.934 0.35332
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5117 on 76 degrees of freedom
## Multiple R-squared: 0.7675, Adjusted R-squared: 0.7338
## F-statistic: 22.8 on 11 and 76 DF, p-value: < 2.2e-16regr18 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Special.promotions*Atmosphere, data=Tiger)
summary(regr18) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Special.promotions * Atmosphere,
## data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.54417 -0.24450 -0.00447 0.26185 1.58053
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.101322 0.483240 -0.210 0.83449
## Price 0.061396 0.072961 0.841 0.40272
## Music.DJ 0.197113 0.068386 2.882 0.00513 **
## Atmosphere 0.233401 0.147581 1.582 0.11792
## Location -0.027380 0.064594 -0.424 0.67286
## Crowd.levels 0.190259 0.072832 2.612 0.01083 *
## Special.promotions -0.008444 0.171699 -0.049 0.96090
## Events 0.045923 0.083715 0.549 0.58492
## Clientele.types 0.195482 0.078922 2.477 0.01547 *
## Venue.staff 0.159991 0.064131 2.495 0.01477 *
## Service.facilities 0.064970 0.069986 0.928 0.35617
## Atmosphere:Special.promotions -0.013301 0.052242 -0.255 0.79971
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5144 on 76 degrees of freedom
## Multiple R-squared: 0.765, Adjusted R-squared: 0.731
## F-statistic: 22.49 on 11 and 76 DF, p-value: < 2.2e-16regr19 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Special.promotions*Location, data=Tiger)
summary(regr19) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Special.promotions * Location,
## data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.52380 -0.24865 0.00554 0.27160 1.50528
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.14798 0.75174 0.197 0.8445
## Price 0.06374 0.07307 0.872 0.3858
## Music.DJ 0.19635 0.06823 2.878 0.0052 **
## Atmosphere 0.20077 0.07999 2.510 0.0142 *
## Location -0.07137 0.20386 -0.350 0.7272
## Crowd.levels 0.19097 0.07280 2.623 0.0105 *
## Special.promotions -0.11657 0.30855 -0.378 0.7066
## Events 0.05291 0.08875 0.596 0.5529
## Clientele.types 0.18992 0.07702 2.466 0.0159 *
## Venue.staff 0.16280 0.06459 2.520 0.0138 *
## Service.facilities 0.06440 0.06997 0.920 0.3603
## Location:Special.promotions 0.01657 0.07192 0.230 0.8184
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5145 on 76 degrees of freedom
## Multiple R-squared: 0.765, Adjusted R-squared: 0.7309
## F-statistic: 22.49 on 11 and 76 DF, p-value: < 2.2e-16regr20 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Special.promotions*Events, data=Tiger)
summary(regr20) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Special.promotions * Events,
## data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.43947 -0.27836 0.00229 0.29139 1.35343
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.57779 0.52638 1.098 0.27581
## Price 0.05791 0.07204 0.804 0.42400
## Music.DJ 0.19971 0.06742 2.962 0.00407 **
## Atmosphere 0.19067 0.07929 2.405 0.01863 *
## Location 0.00119 0.06688 0.018 0.98585
## Crowd.levels 0.17949 0.07238 2.480 0.01535 *
## Special.promotions -0.33791 0.22171 -1.524 0.13163
## Events -0.16748 0.17440 -0.960 0.33992
## Clientele.types 0.17271 0.07708 2.241 0.02797 *
## Venue.staff 0.18313 0.06526 2.806 0.00637 **
## Service.facilities 0.05667 0.06935 0.817 0.41640
## Special.promotions:Events 0.09439 0.06785 1.391 0.16823
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5082 on 76 degrees of freedom
## Multiple R-squared: 0.7706, Adjusted R-squared: 0.7374
## F-statistic: 23.21 on 11 and 76 DF, p-value: < 2.2e-16regr21 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Special.promotions*Clientele.types, data=Tiger)
summary(regr21) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Special.promotions * Clientele.types,
## data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.52247 -0.24500 -0.00971 0.20685 1.65382
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.36489 0.43711 -0.835 0.40647
## Price 0.06694 0.07232 0.926 0.35760
## Music.DJ 0.20104 0.06774 2.968 0.00401 **
## Atmosphere 0.19213 0.07959 2.414 0.01819 *
## Location -0.03932 0.06487 -0.606 0.54621
## Crowd.levels 0.19807 0.07242 2.735 0.00776 **
## Special.promotions 0.09852 0.14501 0.679 0.49896
## Events 0.03076 0.08401 0.366 0.71527
## Clientele.types 0.36525 0.16630 2.196 0.03112 *
## Venue.staff 0.15454 0.06371 2.426 0.01766 *
## Service.facilities 0.07337 0.06977 1.052 0.29631
## Special.promotions:Clientele.types -0.05693 0.04828 -1.179 0.24196
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.51 on 76 degrees of freedom
## Multiple R-squared: 0.769, Adjusted R-squared: 0.7356
## F-statistic: 23 on 11 and 76 DF, p-value: < 2.2e-16regr22 <- lm(Oveerall.Satisfaction ~ Price+Music.DJ+Atmosphere+Location+Crowd.levels+Special.promotions+Events+Clientele.types+Venue.staff+Service.facilities+Events*Clientele.types, data=Tiger)
summary(regr22) ##
## Call:
## lm(formula = Oveerall.Satisfaction ~ Price + Music.DJ + Atmosphere +
## Location + Crowd.levels + Special.promotions + Events + Clientele.types +
## Venue.staff + Service.facilities + Events * Clientele.types,
## data = Tiger)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.5302 -0.2518 0.0011 0.2553 1.5398
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.017026 0.409234 0.042 0.9669
## Price 0.062632 0.072901 0.859 0.3930
## Music.DJ 0.196512 0.068607 2.864 0.0054 **
## Atmosphere 0.201243 0.080073 2.513 0.0141 *
## Location -0.025324 0.066253 -0.382 0.7034
## Crowd.levels 0.190839 0.072819 2.621 0.0106 *
## Special.promotions -0.048197 0.076124 -0.633 0.5285
## Events 0.035414 0.135066 0.262 0.7939
## Clientele.types 0.174639 0.178857 0.976 0.3320
## Venue.staff 0.161338 0.064236 2.512 0.0141 *
## Service.facilities 0.064309 0.070030 0.918 0.3614
## Events:Clientele.types 0.005063 0.050126 0.101 0.9198
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5146 on 76 degrees of freedom
## Multiple R-squared: 0.7648, Adjusted R-squared: 0.7308
## F-statistic: 22.47 on 11 and 76 DF, p-value: < 2.2e-16